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Let f: R--> R be a function defined by f(x) = min{x + 1,|x|+1}; then prove that f(x) is diffrentiable everywhere

Let f: R--> R be a function defined by f(x) = min{x + 1,|x|+1}; then prove that f(x) is diffrentiable everywhere
 

Grade:11

2 Answers

Arun
25758 Points
4 years ago
Dear Meghana
 
This can be seen as problem if arise will be due to modulus function i.e. |x| + 1
 
Now it will be non differentiable at x= 0 but at x = 0 
 
x+ 1 will be taken as main function.
 
hence f(x) is diffrentiable everywhere
Aditya Gupta
2081 Points
4 years ago
the correct answer would be f(x)= x+1 (because |x| greater than equal to x for all x)
so f’(x)=1 and hence it is differentiable everywhere

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